1. Field of Invention
The present invention pertains to automated design and analysis of auctions. More particularly, this invention relates to a method and system for setting an optimal reserve price for an auction.
2. Related Art
A seller who wishes to sell an item, or a set of items, by running an auction has to make a number of decisions. First, he has to choose a format from among a number of alternative formats: English, Dutch, Vickrey, sealed-bid first-price to name a few common formats. Then he has to decide the levels of a number of parameters: reserve price, bid increment, entry fees, lot size etc. A reserve price in an auction for selling an item is the minimum price below which no bids are accepted. If all the submitted bids are below the reserve price, then no sale occurs. Alternative combinations of these decisions typically yield different outcomes from the seller's point of view.
Similarly, a buyer who wishes to purchase an item, or a set of items, by running an auction also has to make a number of decisions. He has to choose a format from among a set of alternative formats. Common auction formats used in purchasing an item include the appropriately modified versions of English, Dutch, Vickrey and sealed-bid first-price auctions. The buyer also has to make decisions on the levels of a number of parameters: reserve price, bid decrement, entry fees, lot size, etc. A reserve price in an auction for purchasing an item is the maximum price above which no bids are accepted. If all the submitted bids are above the reserve price, then no purchase occurs. Alternative combinations of these decisions typically yield different outcomes from the buyer's point of view.
Whether or not a given combination of decisions is better than an alternative combination depends on the specifics of the auction environment. Auction environments are characterized by a number of factors. Some of these factors are observable by the decision-maker and some are inherently unobservable. For example, a seller conducting an auction to sell an item may know the number of potential bidders, but the willingness-to-pay (valuation) of a bidder for the item is typically known by the bidder himself. From the point of view of the seller, the valuation of a bidder is uncertain, or random. Similarly, the bidders' attitudes towards risk and the distribution of bidders' private information affect the bidding behavior and thus the outcome of the auction.
Currently, the decision on the reserve price is left entirely to the person conducting the auction. The reserve price decision is currently guided by rules of thumb, and is error prone. There is little systematic data analysis to guide these decisions. Given the multiplicity of items bought and sold through auctions, it is typically too costly to hire expert analysts to configure the auction procedures for each case. In many markets the factors that affect the auction outcomes, and hence the appropriate reserve price, are seldom fixed, and thus a reserve price which is fixed once-and-for-all is often the wrong one. This invention provides an integrated data collection, modeling, estimation and optimization solution for selecting the reserve price optimally based on structural econometric analysis of available data. Thus, this invention makes it possible for a seller (buyer) to dynamically change the reserve price in response to changing situations.
This invention proposes a system that provides automated decision support for selecting the best reserve price based on structural analysis of data from related auctions to determine the latent elements of the auction environment taking into account the strategic and information conditions with minimal assumptions on the distributions of unobserved random elements.
A seller conducting an auction to sell an item(s) can improve the auction outcome in his favor by selecting the reserve price based on the characteristics of the bidders. Similarly, a buyer conducting an auction to procure an item(s) can improve his expected procurement cost by selecting the reserve price based on the characteristics of the bidders. Bidders' characteristics can be estimated by using structural econometric analysis of bids in past auctions, and the estimated bidder characteristics can be used to estimate the outcomes under alternative levels of the reserve price.
As is known, the outcome of an auction (i.e. who gets what, who pays how much) is determined by bidding behavior of bidders. Bidding behavior depends on, among other factors, the auction rules in that different auction rules induce different behavior on the part of the bidders. A bidder's behavior under a given collection of auction rules in turn is determined by the bidder's private information. The structure of the private information held by the bidders is thus a key factor in evaluating alternative auction rules. This fundamental element of the auction environment is not directly observable and has to be estimated from available data.
Analysis of bidding behavior in auctions and comparison of alternative auction rules in terms of expected outcomes implied by the bidding behavior induced by the bidding rules has been an active area of research in economics. A celebrated result of this body of research is that most common auction formats (including English, sealed-bid first-price, Dutch, Vickrey) are equivalent in terms of expected outcome (expected revenue in the case of a seller, expected procurement cost in the case of a buyer) generated in market environments where the bidders are risk neutral and their private valuations of the item are statistically independent and identically distributed. Furthermore, these auction formats combined with an appropriate reserve price are optimal in the sense that the seller (buyer) cannot achieve a better outcome (expected revenue in the case of a seller, expected procurement cost in the case of a buyer) by using any other selling (buying) procedure. The appropriate reserve price, however, depends on the distribution of bidders' private information. Thus, the well-known theoretical results on optimal reserve price in the economics literature are of little practical use in many decision situations. In particular, the most important factor in the comparison of alternative decisions is the structure of private information of the bidders. This structure is typically unknown by the decision-maker and needs to be estimated from available data. Furthermore, when the said assumptions (risk neutrality, symmetry of bidders, and independence of valuations) are violated, the ranking of alternative auction rules typically depends on the specific structure of valuation distributions and the specific form of the risk attitudes of the bidders. Again, these structural elements of the auction environment are typically unknown by the decision-maker and need to be estimated from available data.
Thus, there exists a need for an automated estimation and optimization solution for selecting the best reserve price. This invention proposes a system that provides automated decision support for selecting the best reserve price based on structural analysis of data from related auctions to determine the latent elements of the auction environment taking into account the strategic and information conditions with minimal assumptions on the distributions of unobserved random elements.